An element in a polynomial representation of an expression.
Default methods, when more specific methods do not work.
Jep function to extract array of coefficients from a polynomial.
The expand(x) command.
Represents an immutable monomial a x^i * y^j * ... * z^k, a constant.
A mutable monomial representing a * x^i * y^j * ... * z^k.
A mutable polynomial representing a + b + c.
Represents a constant.
Represents a function.
Represents a polynomial.
A system for symbolic simplification, expansion and comparision based on conversion to a canonical polynomial representation.
Represents an operator.
Represents a variable.
The simplify(x) command.
PolynomialCreator pc = new PolynomialCreator(jep); Node simp = pc.simplify(node); Node expand = pc.expand(node); boolean flag = pc.equals(node1,node2); int res = pc.compare(node1,node2); PNodeI poly = pc.createPoly(node);
The basic idea is to reduce each equation to a canonical form based on a total ordering of the terms.
For example a polynomial in
x will always be in the form
a+b x+c x^2+d x^3.
This makes comparison of two polynomials easy as it is just necessary to compare term by term, whereas it is dificult
(x+1)*(x-1) without any simplification or reordering is tricky.
As an illustration some of the rules for the ordering are
A polynomial is constructed from a set of monomials by arranging the monomials in order. Likewise a monomial is constructed from a set of variables by arranging the variables in name order.
The algorithm can also work with non-polynomial equations. Functions are order by the name of the function and the ordering of their arguments.
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